Samaras:
Having operated both John Deere and Kubota tractors, I think I understand your feelings. Let me comment a bit on each point:
1. I too feel more tippy on the mid chassis John Deere than on the Kubota's that I have driven, particularly when tipping sideways. I don't think the John Deere is really any more likely to tip over, but rather John Deere has chosen to put the seat up higher for visibility and when you are up higher, it feels more tippy. Now if the rear of the tractor was coming off the ground that is another thing. That simply means the tractor did not have enough rear ballast.
2. The jerkiness you also commented on may be due to the difference in pedal forces between the Kubota and John Deere. The Deere eHydro has much lower pedal forces and if you push the pedal with the same force that you use on your Kubota, then you will experience a jerk because the hydro is very responsive. As others have mentioned, the 3520 does have adjustable aggressiveness levels (similar to Kubota's GST) that allow you to increase or reduce the responsiveness.
Also, mention your experience to the dealer and have the dealer drive the tractor to make sure there isn't a problem.
An additional thought - What range gear were you operating in. I find that A range is best when digging in dirt. B range is a little two fast and will jerk you around when driving over rough ground.
3. If you stalled the 3520, then either the Load Match switch wasn't turned on, or the tractor has a problem. I have never been able to stall a John Deere with an eHydro. I have slipped all four wheels on concrete while pushing and lifting with the bucket. I even tried to stall it by yanking the throttle back to idle while doing this and I could not do it! If the Load Match switch is turned off, then yes this tractor will stall because the hydro in it is the exact same one used in the much heavier 4000 series and 110 TLB. The hydro has enough capacity to bring any 3000 series tractor to stall if Load Match isn't enabled.
Good luck on your future tractor direction!